In-Place Parallel-Partition Algorithms using Exclusive-Read-and-Write Memory

Abstract: We present an in-place algorithm for the partition problem that has linear work and polylogarithmic span. The algorithm uses only exclusive read/write shared variables, and can be implemented using parallel-for-loops without any additional concurrency considerations (i.e., the algorithm is EREW). A key feature of the algorithm is that it exhibits provably optimal cache behavior, up to small-order factors. We also present a second in-place EREW algorithm for the partition problem that has linear work and span $O(\log n \cdot \log \log n)$, which is within an $O(\log\log n)$ factor of the optimal span. By using this low-span algorithm as a subroutine within the cache-friendly algorithm, we are able to obtain a single EREW algorithm that combines their theoretical guarantees: the algorithm achieves span $O(\log n \cdot \log \log n)$ and optimal cache behavior. As an immediate consequence, we also get an in-place EREW quicksort algorithm with work $O(n \log n)$, span $O(\log^2 n \cdot \log \log n)$. Whereas the standard EREW algorithm for parallel partitioning is memory-bandwidth bound on large numbers of cores, our cache-friendly algorithm is able to achieve near-ideal scaling in practice by avoiding the memory-bandwidth bottleneck. The algorithm's performance is comparable to that of the Blocked Strided Algorithm of Francis, Pannan, Frias, and Petit, which is the previous state-of-the art for parallel EREW sorting algorithms, but which lacks theoretical guarantees on its span and cache behavior.